Finite-time Stability Of A Class Of Recurrent Neural Networks With Tunable Activation Functions

In this paper, based on the Lyapuonv finite-time stability theory, we will study a classof recurrent neural networks with the tunable activation functions. The finite-time stabilityof recurrent neural networks and the convergence time are researched.The neural networkshave some tunable parameters. On the one hand, the tunable parameters can improve theconvergence speed of the neural networks. On the other hand, they can improve theanti-interference performance and robustness. Based on the neural network, this paperresearches solving Sylvester equation, solving QP question, solving Time-Varing QPquestion and parameter estimate and energy efficiency optimization of belt conveyors. Thispaper is divided into six sections.Section1is introduction. A brief overview on the development of recurrent neuralnetwork and finite-time stability advance are introduced. Meanwhile, the current advanceof existing problem at this stage is also introduced briefly, and the program of thisdissertation is given too.Section2, we study the problem: Solving time-varying Sylvester equation byrecurrent neural network. At first, based on the finite-time theory and by constructing atunable activation function, we construct a recurrent neural network. Then, the finite-timestability is derived for the proposed neural networks, the upper bounds of the convergencetime are reviewed and the effectiveness of our methods are validated by compared to theexisting neural networks for four aspects: convergent speed, sensitivity to additive noise,conservatism of estimation of the upper bound of the convergent time and conservatism ofZhang neural network design. At last, the simulation results are shown.For the third section, the problem “Finite time dual neural networks with a tunableactivation function for solving quadratic programming problems and its application’’ isstudied. Firstly, in order to solve the Quadratic Programming (QP) problem based on theproposed neural network, the QP problem is translated by Karush-Kuhn-Tucker (KKT)conditions. Secondly, by Lyapunov theorem, the finite-time stability of the proposed neuralnetwork is proved, the actual optimal solutions of the QP problems can be obtained infinite time interval and the upper bound of the convergent time is estimated. Lastly, thefeasibility and superiority of our proposed neural network are present by numericalexamples and K-Winner-Take-All (KWTA) problem.“Solving time-varying quadratic programs based on finite-time Zhang neuralnetworks and their application to robot tracking” is studied in chapter4. At first, the time-varying quadratic program (TVQP) is translated into a problem which can be solvedby the design recurrent neural networks. Then, the problem is solved by based on theneural networks and it is proved that the actual optimal solutions of the TVQP can beobtained in finite time interval and the upper bound of the convergent time is estimated. Atlast, our methods are applied to robot tracking.The chapter five studies the problem: Parameter estimate and energy efficiencyoptimization of belt conveyors based on recurrent neural networks. By the KKT conditionsand the theory of optimal or suboptimal, the parameter estimate problem and six energyefficiency optimization problems are translated into the models which can be solved by theproposed recurrent neural networks. Then, recurrent neural networks are designed to solvethe problems and the optimal or suboptimal solutions of the problems can be obtained infinite-time. At last, numerical simulations show the effectiveness of our methods bycomparing to the existing methods.In the last part, we summarize the whole work of the thesis and point out thedeveloping directions that needs to be further explored in the future.